Topological Methods For Ordinary Differential Equations
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Topological Methods For Ordinary Differential Equations
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Author : Patrick Fitzpatrick
language : en
Publisher: Springer
Release Date : 2006-11-14
Topological Methods For Ordinary Differential Equations written by Patrick Fitzpatrick and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The volume contains the texts of four courses, given by the authors at a summer school that sought to present the state of the art in the growing field of topological methods in the theory of o.d.e. (in finite and infinitedimension), and to provide a forum for discussion of the wide variety of mathematical tools which are involved. The topics covered range from the extensions of the Lefschetz fixed point and the fixed point index on ANR's, to the theory of parity of one-parameter families of Fredholm operators, and from the theory of coincidence degree for mappings on Banach spaces to homotopy methods for continuation principles. CONTENTS: P. Fitzpatrick: The parity as an invariant for detecting bifurcation of the zeroes of one parameter families of nonlinear Fredholm maps.- M. Martelli: Continuation principles and boundary value problems.- J. Mawhin: Topological degree and boundary value problems for nonlinear differential equations.- R.D. Nussbaum: The fixed point index and fixed point theorems.
Topological Methods For Ordinary Differential Equations
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Author : Centro internazionale matematico estivo. Session
language : en
Publisher:
Release Date : 1993
Topological Methods For Ordinary Differential Equations written by Centro internazionale matematico estivo. Session and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Topological Methods In Differential Equations And Inclusions
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Author : Andrzej Granas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topological Methods In Differential Equations And Inclusions written by Andrzej Granas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations.
Topological Methods For Delay And Ordinary Differential Equations
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Author : Pablo Amster
language : en
Publisher: Springer Nature
Release Date : 2024-08-12
Topological Methods For Delay And Ordinary Differential Equations written by Pablo Amster and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-12 with Mathematics categories.
This volume explores the application of topological techniques in the study of delay and ordinary differential equations with a particular focus on continuum mechanics. Chapters, written by internationally recognized researchers in the field, present results on problems of existence, multiplicity localization, bifurcation of solutions, and more. Topological methods are used throughout, including degree theory, fixed point index theory, and classical and recent fixed point theorems. A wide variety of applications to continuum mechanics are provided as well, such as chemostats, non-Newtonian fluid flow, and flows in phase space. Topological Methods for Delay and Ordinary Differential Equations will be a valuable resource for researchers interested in differential equations, functional analysis, topology, and the applied sciences.
Topological Fixed Point Theory Of Multivalued Mappings
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Author : Lech Górniewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 1999
Topological Fixed Point Theory Of Multivalued Mappings written by Lech Górniewicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework.
Topological Methods In The Study Of Boundary Value Problems
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Author : Pablo Amster
language : en
Publisher: Springer
Release Date : 2013-11-30
Topological Methods In The Study Of Boundary Value Problems written by Pablo Amster and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-30 with categories.
This graduate-level textbook presents representative problems in nonlinear analysis by topological methods. The approach is elementary with simple model equations and applications, allowing students to focus on the application of topological methods.
Topological Methods For Differential Equations And Inclusions
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Author : John R. Graef
language : en
Publisher: CRC Press
Release Date : 2018-09-25
Topological Methods For Differential Equations And Inclusions written by John R. Graef and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-25 with Mathematics categories.
Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.
Topological Methods In The Study Of Boundary Value Problems
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Author : Pablo Amster
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-23
Topological Methods In The Study Of Boundary Value Problems written by Pablo Amster and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-23 with Mathematics categories.
This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems. In comparison with other texts in the field, this one has the advantage of a concise and informal style, thus allowing graduate and undergraduate students to enjoy some of the beauties of this interesting branch of mathematics. Exercises and examples are included throughout the book, providing motivation for the reader.
Fixed Points And Topological Degree In Nonlinear Analysis
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Author : Jane Cronin
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-01-05
Fixed Points And Topological Degree In Nonlinear Analysis written by Jane Cronin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-05 with Fixed point theory categories.
The topological methods based on fixed-point theory and on local topological degree which have been developed by Leray, Schauder, Nirenberg, Cesari and others for the study of nonlinear differential equations are here described in detail, beginning with elementary considerations. The reader is not assumed to have any knowledge of topology beyond the theory of point sets in Euclidean n-space which ordinarily forms part of a course in advanced calculus. The methods are first developed for Euclidean n-space and applied to the study of existence and stability of periodic and almost-periodic solutions of systems of ordinary differential equations, both quasi-linear and with ``large'' nonlinearities. Then, after being extended to infinite-dimensional ``function-spaces'', these methods are applied to integral equations, partial differential equations and further problems concerning periodic solutions of ordinary differential equations.
Topological Methods For Differential Equations And Inclusions
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Author : John R. Graef
language : en
Publisher: CRC Press
Release Date : 2018-09-25
Topological Methods For Differential Equations And Inclusions written by John R. Graef and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-25 with Mathematics categories.
Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.